Home Page of Dr. Myron Hlynka,

Queueing Theorist

Co-ordinator, Master of Actuarial Science Program, University of Windsor.
Most recent update: April, 2016.

Statistics Video Courses
Math Institute Videos.
M. Hlynka timetable (January-April, 2016)
- To see Dr. Hlynka's Reasons for Selecting the University of Windsor to Study Undergraduate Mathematics and Statistics, click on
Choose U. of Windsor Math. & Stat.
- To see reasons to study actuarial science at the University of Windsor, see

Visit a collection of queueing theory material and pointers at Myron Hlynka's Queueing Theory Page.

Give an example of a word in the English language with five consecutive vowels.

The answer is QUEUEING!

(Please do NOT use the alternative spelling QUEUING.)

Q: If you had a preemptive priority system with seven low priority customers in the system, and a high priority customer arrived and bumped the low priority customer from service, what name (from a Disney movie) would be appropriate to describe this situation?
A: No Wait and the Seven Dwarfs!

For more queueing levity, click HERE.
For other math humor, visit
Myron Hlynka's Math Jokes.

"Web Resources for Actuarial Exam P" can be found HERE(P).
"Web Resources for Actuarial Exam FM" can be found HERE(FM).
"Web Resources for Actuarial Exam MFE" can be found HERE(MFE).
"Web Resources for Actuarial Exam MLC" can be found HERE(MLC).
"Web Resources for Actuarial Exam C" can be found HERE(C).
For information on courses at the University of Windsor that help to prepare for SOA Actuarial Exams, see
1. http://web2.uwindsor.ca/math/hlynka/UofWindsorcourses.pdf
2. http://web2.uwindsor.ca/math/hlynka/actuarial.html
3. 2016 Exam Dates
4. SOA Exam Approved Calculators.

CORS 2015 Presentation:

CORS 2014 Presentation:

CanQueue 2012 Presentation:

CanQueue 2010 Presentation:

CanQueue 2009 was held in Windsor, Ontario, Canada August 27-28, 2009. See

Dr. Myron Hlynka

Dept. of Math. & Stat.
University of Windsor
Windsor, Ontario, Canada N9B 3P4

Phone (519)-253-3000 Extension 3014
Fax: (519)-971-3649
e-mail: hlynka@uwindsor.ca
URL: http://web2.uwindsor.ca/math/hlynka/index.html
Office Address: 9114 Lambton Tower
For my photo, click HERE.
For a CV, click on
M. Hlynka CV.
For Wintert Term, 2016 (September-December)
I am teaching 65-555 (Regression) and 65-376 (Stochastic Operational Research) and I am supervising 1 PhD student and 4 Master's degree students, and two "Outstanding scholars." I am the academic co-ordinator of the MActSc program. I am the undergraduate advisor. I am also working on various research projects and continue with my regular administrative duties.

Professional Accreditation and Memberships:

  • P. Stat. (Professional Statistician).
    There are only 125 accredited statisticians in Canada.
  • Canadian Operations Research Society (CORS) (This links to the CORS home page.)
  • Statistical Society of Canada (S.S.C.) (This links to the SSC home page.)
  • INstitute For Operations Research and Management Sciences(INFORMS)
    (This links to the INFORMS home page.)
  • American Statistical Association (A.S.A.) (This links to the ASA home page.)
  • Mathematical Association of America (M.A.A.) (This links to the MAA home page.)

  • Research Interests

    My research interests in queueing theory include control of queueing systems, parallel queues, queue joining strategies, queueing applications in health (cholesterol, attention-deficit/hyperactivity disorder), queueing applications in sports (when to remove a goalie in a hockey game), double ended queues, reversible queues, queueing applications in telecommunications, and queueing applications in health services. I also have research interests in inventory theory, robustness, random truncation, Markov Chain Monte Carlo methods, preprocessing, and the "secretary problem."

    Graduate Students Supervised

    1. Andrew LUONG, M.Sc.(Statistics), University of Alberta, 1983
      Master's Paper: Some Results in Reliability Using Death-Immigration and Renewal Processes
    2. Wai-Hang POON, M.Sc.(Computer Science), University of Windsor, 1991, co-supervised with Dr. Henry Toews
      Master's Thesis: Dynamic Scheduling Strategies for Pseudo Parallel Queues: Observing Queues Before Joining
    3. Richard SCHELL, M.Sc. (Statistics), University of Windsor, 1994
      Master's Paper: A Queueing Model for Cholesterol
      (University of Windsor Gold Medalist - October, 1995)
    4. Steve DREKIC, M.Sc. (Statistics), University of Windsor, 1995
      Master's Paper: Conditional Maximum Distributions and Random Truncation
      Currently a professor in the Dept of Statistics and Actuarial Sciences at the University of Waterloo.
    5. Kirk ROY, M.Sc. (Statistics), University of Windsor, 1997.
      Master's Thesis: A Probabilistic Interpretation of Laplace Transforms
      - co-supervised with Dr. Richard Caron
    6. Mathew CHANDLER, M.Sc. (Statistics), University of Windsor, 1997.
      Master's Thesis: A Situational Analysis of the Sacrifice Bunt in Baseball
    7. Luat BUI, M.Sc. (Mathematics), University of Windsor, 1997.
      Master's Thesis: New Results in Partition Theory
    8. Todd BRAITHWAITE, M.Sc. (Statistics), University of Windsor, 1997.
      Master's Thesis: A Two Dimensional Bin Packing Algorithm.
      - co-supervised with Dr. Richard Caron
    9. Wayne HORN, M.Sc. (Statistics), 1999.
      Master's Thesis: Laplace Transforms of Order Statistics of Erlang Random Variables
      - co-supervised with Dr. Percy Brill.
    10. Yingchun LUO M.Sc. (Statistics), 2000.
      Master's Major Paper: A Doubly Stochastic Inventory Model.
    11. Matthew HAEHNEL. M.Sc. (Math), 2001.
      Master's Major Paper: A Modified Runs Test and the Stock Market.
    12. Bashar ZOGHEIB. M.Sc. (Stat), 2002.
      Master's Major Paper: SAS and Approximations to the Standard Normal Cumulative Distribution Function.
    13. Yong Xiang WU. M.Sc. (Stat), 2003.
      Master's Major Paper: M/M/c/c Queueing Systems and Parking Lots.
    14. Huiling XIONG. M.Sc. (Stat), 2003.
      Master's Major Paper: Inequalities for a Parking Lot Queueing Model.
    15. Yi Bei ZHANG. M.Sc. (Stat), 2004. (co-supervised with T. Traynor)
      Master's Major Paper: Convergence and Stochastic Stability of One Step Methods for Stochastic Differential Delay Equations.
    16. Wen MIN. M.Sc. (Stat), 2005.
      Master's Major Paper: vv Exploratory Statistical Study of E-Bay Textbook Auctions.
    17. Xiaoyong WU. Ph.D. (Stat), 2005. (co-supervised with P. Brill)
      Some Retrial Queueing Models.
    18. Jing TANG. M. Sc. (Stat.) 2005. Control of Queues with Unknown Completion Time.
    19. Chinthanie RAMASUNDARAHETTIGE. M.Sc. (Stat). A Comparison of Several Queueing Software Packages. 2006.
      v http://web2.uwindsor.ca/math/hlynka/ramamajorpaper.pdf
    20. Dongfang CHANG. M.Sc. (Stat.) 2006.
      Major Paper: Queues which Form Prior to Opening of Service Facility.
    21. Tolulope SAJOBI. M.Sc. (Stat.) 2008.
      Thesis. Markov Transition Matrices and Fibonacci Numbers (126 pp.)
      (Vanier Scholarship Winner)
    22. Qianying WU. M.Sc. (Stat.) 2008.
      Major Paper: Some Properties of First Passage Distributions.
    23. Waqas ZUBERI. M.Sc. (Stat.) 2009.
      Major Paper: A Survey of Markov Applications to Medical Conditions. 2009.
    24. Rifat JAHAN. M.Sc. (Stat.) 2009.
      Major Paper: Queueing Control and Laplace Transforms.
      -co-supervised with Percy Brill
    25. Shan XU. M.Sc. (Stat.) 2010.
      Major Paper: Some Results on Transient Queues.
    26. Qian JIANG. M.Sc. (Stat.) 2011.
      Major Paper: Construction of Transition Matrices for Reversible Markov Chains
    27. Mubeen HUSSAIN. M.Sc. (Stat.) 2011.
      Major Paper: Time to Ruin for Loss Reserves.
    28. Victoria CHERNOUKHOVA. M.Sc. student. 2012-2013.
      Major Paper: Markov Chain Analysis for Vehicular Left-Turning Lanes
    29. Qianqian WANG. M.Sc. student, 2012-2013.
      Major Paper: Comments on Level Crossing Methods
      co-supervised with Percy Brill
    30. Bingsen YAN. M.Sc. student., 2012-2014.
      Major Paper: Laplace Transforms of Busy Periods in Queues
    31. Zishan HUANG, M.Sc. student 2014-2015 . Major Paper: Probabilistic Laplace Transform Inversion.
    32. Ziwen AN, M.Sc. student 2014-15. Major Paper: Reliability Results using Probabilistic Interpretation of Laplace Transforms.
    33. Chi Ho CHEUNG, PhD student. 2011-. In progress.
      c0-suervised with Percy Brill
    34. Qian JIANG, PhD student. 2011-. On leave.
      co-supervised with Percy Brill
    35. Dongrui LU. M. Sc. student 2015- . In progress.
    36. Chong LIU. M. Sc. student 2015- . In progress.
    37. Xinwei LIU. M. Sc. student 2015- . In progress.
    38. Anthony Wright, M. Sc. student, 2015- . In progress

    Undergraduate NSERC/ MITACS Summer Award Students Supervised

    1. Wai-hang POON, 1989
    2. Karen LUCIER Hill, 1990
    3. Nicole LEMIRE, 1990, co-supervised with Dr. R. Caron
    4. Kar WONG, 1992
    5. Steve DREKIC, 1993
    6. Kirk ROY, 1995, co-supervised with Dr. R. Caron
    7. Jon CASEY, 2002.
    8. Deborah LOACH, 2005, co-supervised with Dr. R. Caron
    9. Laura HURAJT, 2006.
    10. Anna CYLWA, 2007.
    11. Michelle CYLWA, 2008.
    12. Samantha MOLINARO, 2009.
    13. Sheng BI, 2015. (MITACS intern from Nanjing University, July-Sept, 2015)

    Refereed Publications:

    1. Hlynka, M. and Sheahan, J., 1986, Optimal Control Relating to the Excess of one Poisson Process over Another, Utilitas Mathematica, pp. 217-230.
    2. Hlynka, M. and Sheahan, J., 1987, Controlling Rates for a Double Queue, Naval Logistics Research Quarterly, V. 34, pp. 569-577.
    3. Hlynka, M. and Sheahan, J., 1988, The Secretary Problem for a Random Walk, Stochastic Applications and Their Applications, V. 28, pp. 317-325.
    4. Hlynka, M., Sheahan, J. and Wiens, D.P, 1990, On the Choice of Support of Re-Descending Psi-Functions in Linear Models with Asymmetric Error Distributions, Metrika, V. 37, pp. 365-381.
    5. Caron, R.J., Hlynka, M. and McDonald, J.F., 1992, On the Best Case Performance of Hit and Run Methods for Detecting Necessary Constraints, Mathematical Programming V. 54. pp. 233-249.
    6. Khasnabish, B., Ahmadi, M., Hlynka, M. and Shridhar, M., 1993, Trading Nodal Storage Capacity with Incremental Transmission Capacity IEEE Transactions on Communications. Vol. 41, pp. 1147-1150.
    7. Khasnabish, B., Ahmadi, M., Hlynka, M. and Shridhar, M., 1993, Trading Nodal Storage Capacity with Incremental Transmission Capacity in Supra-high-speed Packet-switching Nets, Canadian Journal of Electrical and Computer Engineering, Vol. 18, pp. 71-80.
    8. Hlynka, M. and Wang, T., 1993. Comments on Duality of Queues with Finite Buffer Size, Operations Research Letters, V. 14, pp. 29-33.
    9. Hlynka, M., Stanford, D., Poon, W. and Wang, T., 1994. Observing Queues before Joining, Operations Research, V. 42, pp. 365-342.
    10. Khasnabish, B., Ahmadi, M., Hlynka, M., and Shridhar, M. 1994. Design and Evaluation of a Smart Congestion -Level Indicator for a Large Group of Queues in ATM Networks, Proceedings of 1994 IEEE GLOBECOM, (refereed) V. 1, pp. 156-161.
    11. Stanford, D. and Hlynka, M., 1996. Observing General Service Queues Before Joining, Operations Research Letters, V. 18, pp. 237-245.
    12. M. Hlynka, S. Drekic and G. McPhail, 1997, A Non- Monotone Waiting Time Queueing Model, Utilitas Mathematica, 52, 83-89.
    13. P.H. Brill and M. Hlynka, 1998, A Single Server N-Line Queue in which a Customer May Receive Special Treatment, Stochastic Models. 14, 905-931.
    14. P.H. Brill and M. Hlynka, 2000. "An Exponential Queue with Competition for Service," European Journal Of Operational Research (126)3 (2000) pp. 587-602.
    15. J.C. Fedoruk, D. Paterson, M. Hlynka, K.Y. Fung, M. Gobet, W. Currie, 2002. "Rapid On-Site Defibrillation versus Community Program." Prehospital and Disaster Medicine, V. 17:2, pp. 102-106.
    16. M. Hlynka and L. Mandziuk. 2002. A Queueing Model for Attention- Deficit / Hyperactivity Disorder. Proceedings of SCI 2002, The 6th World Multi-Conference on SYSTEMICS, CYBERNETICS AND INFORMATICS. Orlando, Florida. July 14-16, 2002, Volume IV, 243-248.
    17. P. Brill and M. Hlynka, 2002. A Geometric Interpretation of 2x2 Markov Transition Matrices. Missouri Journal of Mathematical Sciences. Volume 14, 2002. 159-174.
    18. M. Mandelbaum and M. Hlynka, 2003. Job Sequencing Using An Expert. International Journal of Production Economics, 85, 389-401.
    19. M. Hlynka and M. Mandelbaum, 2003. Improving Computer Processing Efficiency by Sequencing. Chapter 33, of monograph High Performance Computing Systems and Applications, Kluwer Publishers, edited by Robert Kent and Todd Sands, pp. 313-327. Proceedings of the 2001 15th Annual Symposium on High Performance Computing Systems and Applications.
    20. X. Wu, M. Hlynka, P. Brill, J. Wang. 2005. "An M/G/1 Retrial Queue with Balking and Retrials during Service." IJOR (International Journal of Operational Research), V. 1, 30-51.
    21. M. Mandelbaum, M. Hlynka, P. Brill. 2007. "Nonhomogeneous Geometric Distributions with Relations to Birth and Death Processes." TOP (Journal of the Spanish Society of Statistics and Operations Research). Volume 15, pp. 281-296.
      If your university has access to Springer publications, you can view a copy at
    22. M. Hlynka and T. Sajobi. 2008. "A Markov Chain Fibonacci Model." Missouri Journal of Mathematical Sciences. Volume 20. No. 3. pp. 186-199.
    23. M. Hlynka, W. Horn, R.Schell. 2008.
      Branching Processes with a Common Extinction Probability.
      International Journal of Pure and Applied Mathematics. V. 45, No. 2, 175-185.
    24. C.K. Cavas, L. Cavas, M.B. Yokes, M. Hlynka, R. Schell, and K. Yurdakoc
      2008. A Novel Application of Queueing Theory on the Caulerpenyne Secreted by Invasive Caulerpa taxifolia (Vahl) C.Agardh (Ulvophyceae, Caulerpales): A Preliminary Study.
      Mediterranean Marine Science, VOLUME 9, NUMBER 1, JUNE 2008. pp. 67-75
    25. M. Mandelbaum and M. Hlynka (2008) Examples of Applications of Queueing Theory in Canada. INFOR, 46(4) 29-46.
    26. M. Hlynka, L. Hurajt, M. Cylwa. 2009. Transient Results for M/M/1/c Queues via Path Counting.
      International Journal of Mathematics in Operational Research. Volume 1, 2009, 20-36.
    27. P.H. Brill, M.L. Huang, M.Hlynka. 2009. Note on an Inventory System with Decay. IAENG International Journal of Applied Mathematics, Volume 39 Issue 3, 171-174.
    28. M. Hlynka, P.H. Brill, W. Horn. 2010. A Laplace Transform Method for Order Statistics of Erlang Random Variables. Probability and Statistics Letters. V. 80, 9-18.
    29. Jerome Cohen, Xue Han, Anca Matei, Vara Parameswaran, Robert Zuniga, Myron Hlynka. 2010. Rats' Visual-Spatial Working Memory: New Object Choice Accuracy as a Function of Number of Objects in the Study Array. Learning and Motivation, v 41 pp. 125-140.
    30. Marvin Mandelbaum and Myron Hlynka. 2009. A History of Queueing in Canada before 1980. INFOR. 47, pp. 335-353.
    31. Hlynka, M. 2011. The M/M/1 Queue. Wiley Encyclopedia of Operations Research and Management Science.
    32. Percy H. Brill, Myron Hlynka. 2012. Server Workload in an M/M/1 Queue with Bulk Arrivals and Special Delays. Applied Mathematics, 2012, 3, 2174-2177. Vol.3 No.12A
    33. Myron Hlynka. 2014. Queueing Theory. Encyclopedia of Social Network Analysis and Mining. Springer. 1472-1483.
    34. Myron Hlynka. 2015. MCMC and the Fibonacci Distribution. Accepted for publication in Communications in Statistics - Simulation and Computation.
    35. Sheng BI and Myron Hlynka. 2016. Preprocessing and Cross Border Traffic. Applied Mathematical Sciences, Vol. 10, 2016, no. 1, 13 - 22

    List of Technical Reports:

    1. Hlynka, M. and Sheahan, J., 1987, Optimal strategies and Poisson Distribution, Technical Report, 4 pp.
    2. Caron, R.J., Hlynka, M., and McDonald, J.F., 1988, Minimizing the Expected Number of Trials in the Coupon Collector's Problem, Windsor Mathematics Report 88-03, 5 pp.
    3. Hlynka, M., 1988, Perishable Inventory Units with an Assignment Time, Windsor Mathematics Report #88-06, (Technical Report), 46 pp.
    4. Hlynka, M. 1988 A Discrete Analog to the Method of Stages, Windsor Mathematics Report #88-11, 17 pp.
    5. Hlynka, M., Sheahan, J.N., and Wiens,D.P, 1989, On Deleting Influential Responses Under a Model of Asymmetric Errors in Regression, University of Alberta Technical Report #89-25, 6 pp.
    6. Hlynka, M. and Poon, W.H., 1989, A Computer Program for Parallel Queues, Windsor Mathematics Report #89-11 (Technical Report) 18 pp.
    7. Hlynka, M. and Poon, W.H., 1989, Properties of the Steady State Probabilities of Two Parallel Queues, Windsor Mathematics Report #89-12, (revised July, 1990), 14 pp.
    8. M. Hlynka and Wang, T., 1990, Comments on Duality of Queues with Finite Buffer Size, Windsor Mathematics Report #90-04, 14 pp.
    9. Wang, T. and Hlynka, M., 1990, Two Parallel Queues with Partial Jockeying, Windsor Mathematics Report, #90-06, 15 pp.
    10. Hlynka, M., Poon, W.H., and Wang, T., 1990, Observing Queues before Joining, Windsor Mathematics Report #90-07, 24 pp.
    11. A.Atmani, R.Caron, M. Hlynka, R.Lashkari, and N. Lemire, 1992, School Bus Scheduling, A Preliminary Report. Windsor Mathematics Report #92-04, 61 pp.
    12. M. Hlynka and C.K. Wong, 1993, An Improved Queue Joining Strategy, Windsor Mathematics Report #93-01, 10 pp.
    13. S.V. Majety, M. Hlynka, and R.S. Lashkari, 1993, Determining the Number of AGV's in Assembly Line Processes.
    14. P.H. Brill and M. Hlynka, 1993, The "Who's Next" Queue with Two Lines, Windsor Mathematics Report, 93-08, 21 pp.
    15. D.A. Stanford and M. Hlynka, 1993, Observing General Service Queues Before Joining, 16 pp.
    16. P.H. Brill and M. Hlynka, 1994, A Single Server N-Line Queue in which a Customer May Receive Special Treatment, Windsor Mathematics Report, 94-03, 21 pp.
    17. M. Hlynka, S. Drekic and G. McPhail, 1994, A Non- Monotone Waiting Time Queueing Model, Windsor Mathematics and Statistics Report 94-05, 10 pp.
    18. L. Mandziuk and M. Hlynka, 1995, A Queueing Model for Attention-Deficit / Hyperactivity Disorder, Windsor Mathematics and Statistics Report 95-02, 18 pp.
    19. M. Hlynka, 1995, Statistical Distributions Arising in Perishable Inventory, Windsor Mathematics and Statistics Report 95-03, 12 pp.
    20. K. Roy and M. Hlynka, 1995, Queueing in APL, Windsor Mathematics and Statistics Report 95-04, 13 pp.
    21. J. Henderson and M. Hlynka, 1995, Risk Aversion and the Selection of a Target for Quality, Windsor Mathematics and Statistics Report 95-05, 11 pp.,
    22. R.J. Caron, M. Hlynka, and K. Roy, 1995, Warranty Expense Forecasting using Operations Research, Report to Chrysler Canada Ltd., Windsor, Ontario. 22 pp. (Propietary)
    23. K. Roy and M. Hlynka, 1995, Queueing Theory Applied to a Traffic Light Problem, Windsor Mathematics and Statistics Report #95-14, 18 pp.
    24. M. Hlynka, 1995, Book Review of "Weighted Approximations in Probability and Statistics", by M. Csorgo and L. Lajos. Interfaces, Sept.-Oct., 1995, pp. 213-214.
    25. P. Brill and M. Hlynka, 1997, "A Geometric Interpretation of Markov Transition Matrices", Windsor Math and Statistics Report, #97-01, 10 pp.
    26. P. Brill and M. Hlynka, 1997, A Multiple Server "Who's Next?" Queue, Windsor Math and Statistics Report, #97-03, 14 pp.
    27. P. Brill and M. Hlynka, 1997, Companion Results to L = lambda W, Windsor Math and Statistics Report, #98-01, 6 pp.
    28. M. Hlynka, W. Horn, R. Schell, 1999. Branching Processes and Fibonacci Numbers. Windsor Math and Statistics Report, #99-02, 9 pp.
    29. K. Roy, M. Hlynka. and R. Caron, 1999. Laplace Transform for the Busy Period of an M/G/1 System, Windsor Math and Statistics Report, #99-05, 7 pp.
    30. J. Casey and M. Hlynka. 2002. The Parrondo Paradox and Queueing. Windsor Math and Statistics Report, #02-02, 13 pp.
    31. M. Hlynka and D. Loach. 2005. Generating Uniform Random Points in a Regular $n$ Sided Polygon. WMSR #05-02. 8 pp.
    32. M. Hlynka. 2006. Introduction to the Statistical Language R. WMSR #06-04. Revised 2008.
    33. M. Hlynka. 2007. Some Examples of Graphics in the Statistical Language R. June 13, 2007.
    34. M. Mandelbaum, M. Hlynka and P.H. Brill, 2006. Nonhomogeneous Geometric Distribution Representations and Queueing. WMSR #06-03.
      (appeared in TOP: Spanish Operational Research Society Journal Volume 15, 2007, pp. 281-296.)
    35. M. Hlynka and L.M. Hurajt. 2006. "M/M/1 Transient Queues and Path Counting." WMSR #06-05.
    36. M. Hlynka and P.H. Brill. 2007. Stability in M/M/1 Queues with Reneging. WMSR #07-09
    37. M. Hlynka and P.H. Brill. 2008. "A Result for a Counter Problem." WMSR #08-01.
    38. M. Hlynka and M. Cylwa. 2009.
      Observations on the Metropolis-Hastings Algorithm." WMSR #09-06.
    39. M. Hlynka and S. Molinaro. 2009.
      "Calculating Transient Probabilities of an M/M/1 Queue: R program and Test Bank." WMSR #09-07.
    40. S. Molinaro and M. Hlynka. 2009.
      Comparing System Times In An Unordered Two Queue network.
      WMSR #09-08.
    41. B. Zogheib and M. Hlynka. 2009.
      Approximations of the Standard Normal Distribution. WMSR #09-09.
    42. S. Molinaro, M. Hlynka, S. Xu. 2011
      Two Unordered Queues. ArXiv 1108.1179, 17 pp. WMSR #11.03
    43. P.H. Brill and M. Hlynka. 2015. Service Time in Variants of Workload-barrier M / G / 1 Queues. WMSR #15-01.


    If you are interested in having Dr. Hlynka as a guest speaker, please contact him by e-mail at hlynka@uwindsor.ca

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